If you set the asscher bezeled but kite set, you'd be able to thin the band substantially while still keeping proportions of the asscher larger or as equal to that of your emeralds.
I think I do have to speak up and say that I don't think the emeralds are suitable sidestones for the asscher. IMO they're just a bit too large, I'd look into getting them recut or use them for a different project.
If you want a 7.5mm wide band but for it not to look to visually 'heavy', you could split it into 3 bands - one forming each 'edge' of the ring (in line with the edge of the asscher) and then the central band with the pavé diamonds, if that makes sense?
Perhaps something inspired by this sort of style?
https://www.furrer-jacot.com/us/wedding/wedding-rings-one-color/platinum/62-52520-0-0
https://www.furrer-jacot.com/us/wedding/multi-colored-wedding-rings/platinum/62-52470-0-0
https://www.furrer-jacot.com/us/wedding/wedding-rings-one-color/palladium/62-51780-0-0
https://www.furrer-jacot.com/us/wedding/gents-only/71-23800-0-0
https://www.furrer-jacot.com/us/wedding/gents-only/71-23790-0-0
https://www.furrer-jacot.com/us/wedding/gents-only/71-28790-0-0